{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T03:00:06Z","timestamp":1780974006781,"version":"3.54.1"},"reference-count":42,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014103","name":"Key Technology Research and Development Program of Shandong","doi-asserted-by":"publisher","award":["2024YFC3307502"],"award-info":[{"award-number":["2024YFC3307502"]}],"id":[{"id":"10.13039\/100014103","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Expert Systems with Applications"],"published-print":{"date-parts":[[2026,7]]},"DOI":"10.1016\/j.eswa.2026.132137","type":"journal-article","created":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T07:38:03Z","timestamp":1774078683000},"page":"132137","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["STMoE: a structured mixture-of-experts framework for robust spatiotemporal series imputation"],"prefix":"10.1016","volume":"319","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-0050-9200","authenticated-orcid":false,"given":"Cang","family":"Qin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-7858-2328","authenticated-orcid":false,"given":"Lina","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6535-477X","authenticated-orcid":false,"given":"Ling","family":"Peng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-6833-1626","authenticated-orcid":false,"given":"Wenyue","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-2565-9834","authenticated-orcid":false,"given":"Meng","family":"Wei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"4","key":"10.1016\/j.eswa.2026.132137_b0005","doi-asserted-by":"crossref","DOI":"10.1145\/3161602","article-title":"Spatio-temporal data mining: A survey of problems and methods","volume":"51","author":"Atluri","year":"2018","journal-title":"ACM Computing Surveys"},{"issue":"7","key":"10.1016\/j.eswa.2026.132137_b0010","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1016\/0098-3004(96)00021-0","article-title":"Multivariate interpolation to incorporate thematic surface data using inverse distance weighting (IDW)","volume":"22","author":"Bartier","year":"1996","journal-title":"Computers and Geosciences"},{"key":"10.1016\/j.eswa.2026.132137_b0015","doi-asserted-by":"crossref","unstructured":"Beretta, L., & Santaniello, A. (2016). Nearest neighbor imputation algorithms: a critical evaluation. {BMC} Medical Informatics Decis. Mak., 16({S-3}), 74. https:\/\/doi.org\/10.1186\/s12911-016-0318-z.","DOI":"10.1186\/s12911-016-0318-z"},{"key":"10.1016\/j.eswa.2026.132137_b0020","unstructured":"Cao, W., Wang, D., Li, J., Zhou, H., Li, Y., & Li, L. (2018). BRITS: bidirectional recurrent imputation for time series.NIPS'18 Proceedings of the 32nd International Conference on Neural Information Processing Systems, Red Hook, NY, USA."},{"issue":"1","key":"10.1016\/j.eswa.2026.132137_b0025","doi-asserted-by":"crossref","first-page":"6085","DOI":"10.1038\/s41598-018-24271-9","article-title":"Recurrent neural networks for multivariate time series with missing values","volume":"8","author":"Che","year":"2018","journal-title":"Scientific reports"},{"issue":"9","key":"10.1016\/j.eswa.2026.132137_b0030","first-page":"4659","article-title":"Bayesian temporal factorization for multidimensional time series prediction","volume":"44","author":"Chen","year":"2022","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"10.1016\/j.eswa.2026.132137_b0035","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1587\/transfun.E92.A.708","article-title":"Fast local algorithms for large scale nonnegative matrix and tensor factorizations","volume":"3","author":"Cichocki","year":"2009","journal-title":"IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E92.A"},{"key":"10.1016\/j.eswa.2026.132137_b0040","unstructured":"Cini, A., Marisca, I., & Alippi, C. (2022). Filling the G_ap_s: Multivariate time series imputation by graph neural networks. International Conference on Learning Representations."},{"key":"10.1016\/j.eswa.2026.132137_b0045","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2023.119619","article-title":"SAITS: Self-attention-based imputation for time series","volume":"219","author":"Du","year":"2023","journal-title":"Expert Systems with Applications"},{"issue":"1","key":"10.1016\/j.eswa.2026.132137_b0050","article-title":"Switch transformers: Scaling to trillion parameter models with simple and efficient sparsity","volume":"23","author":"Fedus","year":"2022","journal-title":"Journal of Machine Learning Research"},{"key":"10.1016\/j.eswa.2026.132137_b0055","article-title":"Filling the missings: Spatiotemporal data imputation by conditional diffusion","author":"He","year":"2025","journal-title":"International Joint Conference on Artificial Intelligence"},{"issue":"10","key":"10.1016\/j.eswa.2026.132137_b0060","doi-asserted-by":"crossref","first-page":"5388","DOI":"10.1109\/TKDE.2023.3333824","article-title":"Spatio-temporal graph neural networks for predictive learning in urban computing: A survey","volume":"36","author":"Jin","year":"2024","journal-title":"IEEE Transactions on Knowledge and Data Engineering"},{"key":"10.1016\/j.eswa.2026.132137_b0065","doi-asserted-by":"crossref","unstructured":"Jing, B., Zhou, D., Ren, K., & Yang, C. (2024). Causality-aware spatiotemporal graph neural networks for spatiotemporal time series imputation. CIKM '24 Proceedings of the 33rd ACM International Conference on Information and Knowledge Management, New York, NY, USA.","DOI":"10.1145\/3627673.3679642"},{"key":"10.1016\/j.eswa.2026.132137_b0070","unstructured":"Lepikhin, D., Lee, H., Xu, Y., Chen, D., Firat, O., Huang, Y., Krikun, M., Shazeer, N., & Chen, Z. (2021). GS}hard: Scaling Giant Models with Conditional Computation and Automatic Sharding. International Conference on Learning Representations."},{"key":"10.1016\/j.eswa.2026.132137_b0075","doi-asserted-by":"crossref","DOI":"10.1016\/j.sigpro.2025.110183","article-title":"Asynchronous graph generator","volume":"238","author":"Ley","year":"2026","journal-title":"Signal Processing"},{"key":"10.1016\/j.eswa.2026.132137_b0080","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2025.129140","article-title":"Missing traffic data imputation with a conditional diffusion framework","volume":"296","author":"Li","year":"2026","journal-title":"Expert Systems with Applications"},{"key":"10.1016\/j.eswa.2026.132137_b0085","unstructured":"Li, Y., Yu, R., Shahabi, C., & Liu, Y. (2018). Diffusion convolutional recurrent neural network: Data-driven traffic forecasting. International conference on learning representations."},{"key":"10.1016\/j.eswa.2026.132137_b0090","doi-asserted-by":"crossref","unstructured":"Liang, G., Tiwari, P., Nowaczyk, S. l., & Byttner, S. (2024). Higher-order spatio-temporal physics-incorporated graph neural network for multivariate time series imputation. CIKM '24 Proceedings of the 33rd ACM International Conference on Information and Knowledge Management, New York, NY, USA.","DOI":"10.1145\/3627673.3679775"},{"key":"10.1016\/j.eswa.2026.132137_b0095","article-title":"Directly modeling missing data in sequences with RNNs: Improved classification of clinical time series","author":"Lipton","year":"2016","journal-title":"Machine Learning in Health Care"},{"key":"10.1016\/j.eswa.2026.132137_b0100","doi-asserted-by":"crossref","unstructured":"Liu, M., Huang, H., Feng, H., Sun, L., Du, B., & Fu, Y. (2023). PriSTI: A conditional diffusion framework for spatiotemporal imputation. 2023 IEEE 39th International Conference on Data Engineering (ICDE), 1927-1939.","DOI":"10.1109\/ICDE55515.2023.00150"},{"key":"10.1016\/j.eswa.2026.132137_b0105","article-title":"Learning to reconstruct missing data from spatiotemporal graphs with sparse observations","author":"Marisca","year":"2022","journal-title":"Advances in Neural Information Processing Systems"},{"key":"10.1016\/j.eswa.2026.132137_b0110","doi-asserted-by":"crossref","unstructured":"Nie, T., Qin, G., Ma, W., Mei, Y., & Sun, J. (2024). ImputeFormer: Low rankness-induced transformers for generalizable spatiotemporal imputation. KDD '24 Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, New York, NY, USA.","DOI":"10.1145\/3637528.3671751"},{"key":"10.1016\/j.eswa.2026.132137_b0115","doi-asserted-by":"crossref","DOI":"10.1016\/j.trc.2022.103737","article-title":"Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns","volume":"141","author":"Nie","year":"2022","journal-title":"Transportation Research Part C: Emerging Technologies"},{"key":"10.1016\/j.eswa.2026.132137_b0120","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2024.123654","article-title":"Imputation of data missing not at random: Artificial generation and benchmark analysis","volume":"249","author":"Pereira","year":"2024","journal-title":"Expert systems with applications"},{"issue":"4","key":"10.1016\/j.eswa.2026.132137_b0125","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1016\/j.cageo.2010.10.010","article-title":"Parallel ordinary kriging interpolation incorporating automatic variogram fitting","volume":"37","author":"Pesquer","year":"2011","journal-title":"Computers and Geosciences"},{"key":"10.1016\/j.eswa.2026.132137_b0130","article-title":"Scaling vision with sparse mixture of experts","author":"Ruiz","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"key":"10.1016\/j.eswa.2026.132137_b0135","unstructured":"Shazeer, N., Mirhoseini, A., Maziarz, K., Davis, A., Le, Q. V., Hinton, G. E., & Dean, J. (2017). Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer. 5th International Conference on Learning Representations, {ICLR} 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings."},{"key":"10.1016\/j.eswa.2026.132137_b0140","series-title":"The Eleventh International Conference on Learning Representations","article-title":"Multivariate time-series imputation with disentangled temporal representations","author":"Shuai","year":"2023"},{"key":"10.1016\/j.eswa.2026.132137_b0145","series-title":"CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation","author":"Tashiro","year":"2021"},{"issue":"3","key":"10.1016\/j.eswa.2026.132137_b0150","first-page":"1","article-title":"mice: Multivariate imputation by chained equations in R","volume":"45","author":"van Buuren","year":"2011","journal-title":"Journal of Statistical Software"},{"key":"10.1016\/j.eswa.2026.132137_b0155","unstructured":"Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L., & Polosukhin, I. (2017). Attention is all you need. NIPS'17 Proceedings of the 31st international conference on neural information processing systems, Red Hook, NY, USA."},{"key":"10.1016\/j.eswa.2026.132137_b0160","doi-asserted-by":"crossref","unstructured":"Wang, D., Yan, Y., Qiu, R., Zhu, Y., Guan, K., Margenot, A., & Tong, H. (2023). Networked time series imputation via position-aware graph enhanced variational autoencoders. KDD '23 Proceedings of the 29th ACM SIGKDD conference on knowledge discovery and data mining, New York, NY, USA.","DOI":"10.1145\/3580305.3599444"},{"key":"10.1016\/j.eswa.2026.132137_b0165","unstructured":"Wu, Y., Zhuang, D., Labbe, A., & Sun, L. (2020). Inductive graph neural networks for spatiotemporal kriging. CoRR, abs\/2006.07527. https:\/\/arxiv.org\/abs\/2006.07527."},{"key":"10.1016\/j.eswa.2026.132137_b0170","doi-asserted-by":"crossref","DOI":"10.1016\/j.inffus.2024.102292","article-title":"Hierarchical spatio-temporal graph convolutional neural networks for traffic data imputation","volume":"106","author":"Xu","year":"2024","journal-title":"Information Fusion"},{"key":"10.1016\/j.eswa.2026.132137_b0175","unstructured":"Yoon, J., Jordon, J., & van der Schaar, M. (2018, 10--15 Jul). GAIN: Missing data imputation using generative adversarial nets. Proceedings of machine learning research proceedings of the 35th international conference on machine learning."},{"issue":"1","key":"10.1016\/j.eswa.2026.132137_b0180","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s00704-012-0723-x","article-title":"Comparison of missing value imputation methods in time series: The case of Turkish meteorological data","volume":"112","author":"Yozgatligil","year":"2013","journal-title":"Theoretical and applied climatology"},{"key":"10.1016\/j.eswa.2026.132137_b0185","article-title":"Temporal regularized matrix factorization for high-dimensional time series prediction","author":"Yu","year":"2016","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"4","key":"10.1016\/j.eswa.2026.132137_b0190","doi-asserted-by":"crossref","first-page":"2645","DOI":"10.1007\/s11063-020-10404-7","article-title":"Semi-supervised classification of graph convolutional networks with laplacian rank constraints","volume":"54","author":"Zhang","year":"2022","journal-title":"Neural Processing Letters"},{"key":"10.1016\/j.eswa.2026.132137_b0195","doi-asserted-by":"crossref","DOI":"10.1016\/j.inffus.2023.102038","article-title":"Semantic understanding and prompt engineering for large-scale traffic data imputation","volume":"102","author":"Zhang","year":"2024","journal-title":"Information Fusion"},{"key":"10.1016\/j.eswa.2026.132137_b0200","doi-asserted-by":"crossref","unstructured":"Zhao, X., & Tang, J. (2017). Modeling temporal-spatial correlations for crime prediction. CIKM '17 Proceedings of the 2017 ACM on conference on information and knowledge management, New York, NY, USA.","DOI":"10.1145\/3132847.3133024"},{"key":"10.1016\/j.eswa.2026.132137_b0205","doi-asserted-by":"crossref","unstructured":"Zheng, Y., Yi, X., Li, M., Li, R., Shan, Z., Chang, E., & Li, T. (2015). Forecasting fine-grained air quality based on big data. KDD '15 Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, New York, NY, USA.","DOI":"10.1145\/2783258.2788573"},{"key":"10.1016\/j.eswa.2026.132137_b0210","series-title":"Proceedings of the IEEE\/CVF conference on computer vision and pattern recognition (CVPR)","article-title":"Task-customized mixture of adapters for general image fusion","author":"Zhu","year":"2024"}],"container-title":["Expert Systems with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S095741742601050X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S095741742601050X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T02:42:59Z","timestamp":1780972979000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S095741742601050X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7]]},"references-count":42,"alternative-id":["S095741742601050X"],"URL":"https:\/\/doi.org\/10.1016\/j.eswa.2026.132137","relation":{},"ISSN":["0957-4174"],"issn-type":[{"value":"0957-4174","type":"print"}],"subject":[],"published":{"date-parts":[[2026,7]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"STMoE: a structured mixture-of-experts framework for robust spatiotemporal series imputation","name":"articletitle","label":"Article Title"},{"value":"Expert Systems with Applications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.eswa.2026.132137","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"132137"}}